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Question

If the line 2x+y+k=0 is a normal to the parabola y2+8x=0 then k= ?

A
16
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B
8
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C
24
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D
24
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Solution

The correct option is D 24
For a line to be normal to a parabola we must have c=2amam3
where m=slope of line, C=y intercept of line and a is related to parabola
Given 2x+y+k=0 is normal to the parabola y2+8x=0
so,y=2xkandy2=8kwhere,m=2anda=2so,k=2amam3k=2(2)(2)(2)(2)3k=24

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